Question: Solve for $x$ and $y$ using elimination. ${2x+2y = 24}$ ${-5x-2y = -48}$
Explanation: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the equations together. Notice that the terms $2y$ and $-2y$ cancel out. $-3x = -24$ $\dfrac{-3x}{{-3}} = \dfrac{-24}{{-3}}$ ${x = 8}$ Now that you know ${x = 8}$ , plug it back into $\thinspace {2x+2y = 24}\thinspace$ to find $y$ ${2}{(8)}{ + 2y = 24}$ $16+2y = 24$ $16{-16} + 2y = 24{-16}$ $2y = 8$ $\dfrac{2y}{{2}} = \dfrac{8}{{2}}$ ${y = 4}$ You can also plug ${x = 8}$ into $\thinspace {-5x-2y = -48}\thinspace$ and get the same answer for $y$ : ${-5}{(8)}{ - 2y = -48}$ ${y = 4}$